Unit 3
The title of Unit 3 in AP Stats
Collecting data
The title of Unit 4 in AP Stats
Probability, Random Variables, and Probability Distributions
The title of Unit 5 in AP Stats
Sampling distributions
The title of Unit 6 and 7 in AP Stats?
Inference for Categorical Data: Proportions
Inference for Quantitative Data: Means
The titles of Units 8 and 9 in AP Stats?
Inference for Categorical Data: Chi-Square
Inference for Quantitative Data: Slopes
What is the best way to collect data?
Random sample
What is the addition rule?
The probability of A or B is equal to the probability of A, multiplied by the probability of B, and subtracted by the probability of A and B.
What is the central limit theorem?
When you take sufficiently large random samples from any population, the distribution of their sample means will approximate a normal distribution (a bell curve), regardless of the original population's distribution.
What is a Type 1 Error?
Occurs in statistics when a researcher incorrectly rejects a true null hypothesis, concluding there is a significant effect or difference when none actually exists.
When do you use a Goodness of Fit test?
What are the four biases when sampling?
Undercoverage, Nonresponse, Response, Voluntary response
What are mutually exclusive events?
Mutually exclusive events are two or more outcomes that cannot happen simultaneously in a single trial.
How can you tell if a point estimate is unbiased?
An estimator is unbiased if the average of all possible sample estimates equals the true parameter, while a biased estimator systematically deviates from the true parameter.
How do you justify a claim about a population mean based on a confidence interval?
Compare the claimed value to the interval's range. If the claimed value falls inside the interval, the claim is plausible. If it falls entirely outside, the claim is not supported by the data at that confidence level.
How do you calculate Expected Counts in two-way tables?
Multiply the row total for that specific cell by its column total, and then divide by the overall grand total.
What are the four principles of experimental design?
Randomization, Replication, Control, Blocking
What are the parameters for a binomial distribution?
Binary outcome - success or fail
Independent - outcome of one trial does not affect the other
N- fixed number of trials
S- Success probability is the same for every trial
Which sampling distribution uses quantitative data, and which uses categorical?
The sample mean will use quantitative
The sample proportion will use categorical
What is the difference between a parameter and a statistic?
A parameter describes a population, and a statistic describes a sample.
How do you test for the slope of a regression model?
Testing the slope of a regression model involves checking if the independent variable has a statistically significant relationship with the dependent variable. This is primarily done using a t-test, where you calculate a t-statistic by dividing your estimated slope coefficient by its standard error.
What two questions must you ask before making a statistical inference?
Was there random selection? Was there random assignment?
A fair die is rolled 3 times. The first 2 rolls resulted in 2 fives. What is the probability of not rolling 5 on the next roll?
What happens on the first two rolls does not affect the chance of getting a 5 again. (5/6)
If a population has a mean of 100 and a standard dev of 20, drawing samples of size n=16 results in a sampling distribution with what new mean and standard dev?
SD=5
Mean=100
What test do you use for a difference in population means?
Use a two-sample t-test
(Or a z-test if the population standard deviation is known.)